The integral of e^U with respect to U is simply e^U + C, where C is the constant of integration.
To see why this is the case, consider the derivative of e^U with respect to U:
d/dU (e^U) = e^U
Thus, the antiderivative of e^U is simply e^U + C. To check this, we can take the derivative of e^U + C with respect to U:
d/dU (e^U + C) = e^U
which confirms that it is indeed the antiderivative of e^U.
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